"At that time lived Jesus, a wise man, if he may be called a man; for he performed many wonderful works. He was a teacher of such men as received the truth with pleasure. He drew over to him many Jews and Gentiles. This was the Christ. And when Pilate, at the instigation of the chief men among us, had condemned him to the cross, they who before had conceived an affection for him did not cease to adhere to him. For on the third day he appeared to them alive again, the divine prophets having foretold these and many other wonderful things concerning him. And the sect of christians, so called from him, subsists to this time."

— Antiquities XVIII, Ch. 3, sec. 3

Problems with the Testimonium

Although apologists sometimes bring this up in response to claims that there is no independent verification of the existence of Jesus, Josephus was born around 37 CE, which is after the purported life of Jesus. Thus, Josephus was neither a contemporary nor an eyewitness, but was reporting information received from others. The actual Testimonium Flavianum appears in Antiquities of the Jews which was published c. 94 CE, 60 years after the purported death of Jesus.

Additionally, this passage is largely considered to be a late Christian interpolation. While scholars used to think that the entire passage was a forgery written in the 4th century, they now believe that the Testimonium was based on an authentic core but was embellished by Christian writers. That is, Josephus did write something about Jesus but whatever it was, it was massively embellished by later Christians.

There are several reasons for considering this passage to be a forgery:

Although the church fathers were quite fond of quoting passages which supported Christianity, since this passage would seem to be the proverbial "nail in the coffin" for doubters, and since early church fathers were very familiar with the works of Josephus, it's very strange indeed that not a single one mentions this quote until Eusebius does in the fourth century. Eusebius is considered the most likely candidate for the creator of this passage and, indeed, he is well-known as believing that a little white lie was justified if it furthered the cause of Christianity. Furthermore, Origen, the famous early Christian apologist quotes extensively from Josephus' works, yet he never mentions this passage.

The passage comes in the middle of a collection of stories about calamities that happened to the Jews. The crucifixion of Jesus would not have been considered a Jewish calamity.

The passage interrupts the normal flow of the text. When the passage is removed, the end of the paragraph before it and the beginning of the paragraph after it merge perfectly.

Josephus was an Orthodox Jew and remained one his entire life. He would have never said such glowing things about Jesus. Indeed, he never would have called him "Christ" and yet remained a Jew his whole life.

Although Josephus reports the miracles of a number of other "prophets", he never once mentions any of Jesus' miracles. Whenever he writes about other prophets he blames them for famines, disease, wars, etc. and even calls them "false prophets". He never does so with Jesus, even though he should've thought such things seeing as he was a Jew.

The last line of the passage, "...subsists to this time", implies that the passage was written a long time after the events in question. Josephus himself, who lived so close to the time of Jesus, would never have written such a thing.

Other Josephus quotes

Another quote from Josephus that's used by Christians is the following:

"Festus was now dead, and Albinus was put upon the road; so he [Ananus, the Jewish high priest] assembled the sanhedrin of judges, and brought before them the brother of Jesus, him called Christ, whose name was James, and some others. And when he had formed an accusation against them as breakers of the law, he delivered them to be stoned...."

This quote isn't as obviously forged as the Testimonium, however there are good reasons to believe that it is:

Josephus was writing for a Roman audience. A Roman audience would not have been familiar with Jewish beliefs concerning the Messiah. Indeed, they probably wouldn't even have known what the word "Christ" meant. To throw such a description in without any explanation would have confused the readers.

Why would Josephus mention Jesus before the person that the passage is actually about? On the other hand, if this were a Christian interpolation it would make sense to have Jesus' name be in the place of status.

The original Greek wording of the passage itself is extremely similar to Matthew 1:16. For an Othodox Jew this would be extremely unlikely.

After reading the rest of the text of this passage we find that the Jews were so angry about the stoning of James that they they demanded that King Agrippa fire Ananus. Why would the Jews be angered over the killing of a Christian, since Christians were seen as heathens by the Jews?